Question

12. An item was sold at a loss of 20%. Had it been sold for Rs. 50

more then, the profit would have been 5%. What is the cost
price of the item?​

Answer 1

Given:

An item was sold at a loss of 20%.

If the item is sol for Rs. 50 more then, the profit would have been 5%.

To find:

The cost price of the item.

Solution:

Let x be the cost price of the item.

The item was sold at a loss of 20%. Then selling selling price is:

`S.P.=x-(20)/(100)x`

`S.P.=x-0.2x`

`S.P.=0.8x`

If a the item is sold for 5% profit, then the selling price is:

`S.P.=x+(5)/(100)x`

`S.P.=x+0.05x`

`S.P.=1.05x`

It is given that, if the item is sol for Rs. 50 more then, the profit would have been 5%. So,

`0.8x+50=1.05x`

`50=1.05x-0.8x`

`50=0.25x`

Divide both sides by 0.25.

`(50)/(0.25)=x`

`200=x`

Therefore, the cost price of the item is Rs. 200.